{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "569d620b-882a-4d90-a82a-e0c2bb85de9d",
   "metadata": {},
   "source": [
    "\n",
    "姚端正、周国全、贾俊基《数学物理方法》第四版P.275\n",
    "\n",
    "里兹法，正弦函数系，重解例题3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e9220533-845d-4da3-88cf-4e204859b2e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  # 导入sympy 包中所有的函数\n",
    "from sympy.abc import x # 引入默认的符号变量\n",
    "c0,c1,c2,lamd = symbols('c0 c1 c2 lambda') # 自定义符号变量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b1db7b4c-a630-474c-8c8a-0e2f2e33cc43",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = c0*sin(x*pi)+c1*sin(2*x*pi)+c2*sin(3*x*pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "81a5c4fa-ff42-41c2-ba96-ca44ec677482",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\pi^{2} c_{0}^{2}}{2} + 2 \\pi^{2} c_{1}^{2} + \\frac{9 \\pi^{2} c_{2}^{2}}{2} - \\lambda \\left(\\frac{c_{0}^{2}}{2} + \\frac{c_{1}^{2}}{2} + \\frac{c_{2}^{2}}{2}\\right)$"
      ],
      "text/plain": [
       "pi**2*c0**2/2 + 2*pi**2*c1**2 + 9*pi**2*c2**2/2 - lambda*(c0**2/2 + c1**2/2 + c2**2/2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phi  = integrate(diff(y,x)**2,(x, 0, 1)) - lamd* integrate(y**2,(x, 0, 1))\n",
    "Phi "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "25edbd4e-f5cc-4198-9adc-727b92971e53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - c_{0} \\lambda + \\pi^{2} c_{0}$"
      ],
      "text/plain": [
       "-c0*lambda + pi**2*c0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq0= diff(Phi,c0)\n",
    "eq0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "69f46e53-7489-42ea-988c-46b5bed6d127",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - c_{1} \\lambda + 4 \\pi^{2} c_{1}$"
      ],
      "text/plain": [
       "-c1*lambda + 4*pi**2*c1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1= diff(Phi,c1)\n",
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f61235f5-dcbc-4e77-a3d9-80665c175883",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - c_{2} \\lambda + 9 \\pi^{2} c_{2}$"
      ],
      "text/plain": [
       "-c2*lambda + 9*pi**2*c2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2= diff(Phi,c2)\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "19071805-db55-4ac0-b6d1-99449c30a5e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0, 0],\n",
       "[0, 0, 0],\n",
       "[0, 0, 0]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c=zeros(3)\n",
    "matrix_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "de5a1f7c-c568-49d8-9a61-42411ed5c9dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [c0,c1,c2]\n",
    "eqs = [eq0,eq1,eq2]\n",
    "for i in [0,1,2]:\n",
    "    for Phi in [0,1,2]:\n",
    "        matrix_c[i,Phi]= expand(eqs[i]).coeff(c[Phi])\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "26353137-749f-4f00-8fbc-7df8633c1c72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\lambda + \\pi^{2} & 0 & 0\\\\0 & - \\lambda + 4 \\pi^{2} & 0\\\\0 & 0 & - \\lambda + 9 \\pi^{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-lambda + pi**2,                 0,                 0],\n",
       "[              0, -lambda + 4*pi**2,                 0],\n",
       "[              0,                 0, -lambda + 9*pi**2]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "41ea76a9-df1f-4662-b538-903745ae24d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\lambda^{3} + 14 \\pi^{2} \\lambda^{2} - 49 \\pi^{4} \\lambda + 36 \\pi^{6}$"
      ],
      "text/plain": [
       "-lambda**3 + 14*pi**2*lambda**2 - 49*pi**4*lambda + 36*pi**6"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4b7aea0c-06b2-4aec-a70b-83b5fa415006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[pi**2, 4*pi**2, 9*pi**2]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd = solve(matrix_c.det(),lamd)\n",
    "#sol_lamd.sort() # 排序\n",
    "sol_lamd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1aed06f5-f346-4638-8e63-34717f301f01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\pi^{2}$"
      ],
      "text/plain": [
       "pi**2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2805e586-4b89-4da4-8641-9284c575db05",
   "metadata": {},
   "outputs": [],
   "source": [
    "condition = integrate(y*y,(x, 0, 1)) -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f5f452d0-820a-46ce-927b-22cb3c1e44eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(2), 0, 0), (sqrt(2), 0, 0)]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_1=[eq0.subs(lamd,sol_lamd[0]), eq1.subs(lamd,sol_lamd[0]),\n",
    "       eq2.subs(lamd,sol_lamd[0]),condition]\n",
    "c_sols_1 = solve(eqs_1, c0,c1,c2)\n",
    "c_sols_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "217615b0-b8c5-4d71-8649-cf10c54fa08a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, -sqrt(2), 0), (0, sqrt(2), 0)]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_2=[eq0.subs(lamd,sol_lamd[1]), eq1.subs(lamd,sol_lamd[1]),\n",
    "       eq2.subs(lamd,sol_lamd[1]),condition]\n",
    "c_sols_2 = solve(eqs_2, c0,c1,c2)\n",
    "c_sols_2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "be5f236f-e65e-4833-ab5f-0b78eb28eb7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0, -sqrt(2)), (0, 0, sqrt(2))]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_3=[eq0.subs(lamd,sol_lamd[2]), eq1.subs(lamd,sol_lamd[2]),\n",
    "       eq2.subs(lamd,sol_lamd[2]),condition]\n",
    "c_sols_3 = solve(eqs_3, c0,c1,c2)\n",
    "c_sols_3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6ef2fbce-3548-4085-897c-716e5217dd7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x24375fc1350>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_1=y.subs([(c0,c_sols_1 [0][0]), (c1,c_sols_1 [0][1]),(c2,c_sols_1 [0][2])])# 基态试探解\n",
    "y_ex_1= sqrt(2) *sin(pi* x) # 基态精确解\n",
    "plot(y_1,y_ex_1,(x,0,1)) # ,legend=True\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "21b0d17d-aef0-4327-b326-c47f59d3bc22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x2437f6c6690>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_2 = y.subs([(c0,c_sols_2 [0][0]), (c1,c_sols_2 [0][1]), (c2,c_sols_2 [0][2])])# 第一激发态试探解\n",
    "y_ex_2 = sqrt(2) *sin(2*pi* x) # 第一激发态精确解\n",
    "plot(y_2,y_ex_2,(x,0,1)) # ,legend=True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "13120c2f-2c4c-4c9f-a458-092f4e64d535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x2437f30d950>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_3 = y.subs([(c0,c_sols_3 [0][0]), (c1,c_sols_3 [0][1]), (c2,c_sols_3 [0][2])]) # 第二激发态试探解\n",
    "y_ex_3 = sqrt(2) *sin(3*pi* x) # 第二激发态精确解\n",
    "plot(y_3, y_ex_3, (x,0,1)) # ,legend=Truev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c5ed5b50-676c-4946-ad6c-5c4e0d3bf841",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 88.8264396098042$"
      ],
      "text/plain": [
       "88.8264396098042"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(sol_lamd[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fcfa79e3-0169-4bee-96ff-45ad12375e64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(c_sols_3[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3d26fe62-b3c5-4d18-af81-3d127fc58f6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -13.3037104471$"
      ],
      "text/plain": [
       "-13.3037104471000"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N((3*3.14159)**2)-102.13\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e8ee0ab3-e904-4325-87bf-0ec5efbe66c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 350x262.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scienceplots # 导入'science'画图模块\n",
    "plt.style.use('science') # 采用'science'画图模块\n",
    "fig, ax = plt.subplots() # 建立画布\n",
    "x = np.linspace(0,1,100) # x轴点数\n",
    "c0 = -4.40\n",
    "c1 = -4.99\n",
    "c2 = 4.99\n",
    "y1 = x*(x-1)*(c0+c1*x+c2*x**2) # 近似解\n",
    "y2 = np.sqrt(2) *np.sin(np.pi* x) # 精确解\n",
    "ax.plot(x,y1,linewidth = '0.7',label=r'Approximate solution',color = 'k',linestyle='--') \n",
    "ax.plot(x,y2,linewidth = '0.7',label=r'Exact solution',color = 'k') \n",
    "ax.set_xlabel('$x$') # 设置横坐标名称\n",
    "ax.set_ylabel('$y(x)$') # 设置总坐标名称\n",
    "ax.spines['right'].set_visible(False) # 不显示右边框\n",
    "ax.spines['top'].set_visible(False) # 不显示上边框\n",
    "ax.legend() # 显示标签\n",
    "visible_ticks = { # 设定参数以不显示上和右刻度\n",
    "   \"top\": False,\n",
    "   \"right\": False\n",
    "}\n",
    "ax.tick_params(axis=\"both\", which=\"both\", **visible_ticks) # 去处上和右刻度\n",
    "fig.savefig('Ritz_fig３.png',dpi=600) # 保存图片\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6f9d9d9f-8adc-4799-a59a-427b20978ab6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3.14159265358979$"
      ],
      "text/plain": [
       "3.14159265358979"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08438db2-39a5-4fd0-8a83-a31336e545fc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
